Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials. (English) Zbl 0927.65097

Paternoster, B.

Appl. Numer. Math. 28, No. 2-4, 401-412 (1998).

The paper is concerned with initial value problems for ordinary differential equations (ODEs) whose solutions are a priori known to oscillate with a known frequency. Runge-Kutta methods are applied to first-order problems and Runge-Kutta-Nyström methods to second-order problems. P. Albrecht’s approach [SIAM J. Numer. Anal. 24, 391-406 (1987; Zbl 0617.65067); Teubner-Texte Math. 104, 8-18 (1988; Zbl 0682.65041)] is considered and the concept of trigonometric order of the method is used. The Runge-Kutta and Runge-Kutta-Nyström methods derived in this paper have low orders (1 or 2) and integrate trigonometric polynomials exactly. Two numerical examples are performed for comparison to others-Runge-Kutta-Nyström methods.

Reviewer: Iulian Coroian (Baia Mare)

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
34C25	Periodic solutions to ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

initial value problems; Runge-Kutta-Nyström methods; periodic solution; first-order problems; second-order problems; trigonometric polynomials; numerical examples

Citations:

Zbl 0617.65067; Zbl 0682.65041

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